Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
768 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 272 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×#1039 | C2 | semidirect |
| 3. C2×C4×C5×Dic5 | C2 | semidirect |
| 4. C2×#87780 | C2 | semidirect |
| 6. #11716973 | C2 | direct (N × H) |
| 12. C2×C4×C5×D5 | C4 | semidirect |
| 14. C4×#1039 | C22 | semidirect |
| 15. C4×C5×Dic5 | C22 | semidirect |
| 16. #87780 | C22 | semidirect |
| 32. C4×C5×D5 | C2×C4 | semidirect |
| 44. C2×C4×Dic5 | D5 | semidirect |
| 70. C2×C4×D5 | Dic5 | semidirect |
| 80. C4×Dic5 | C2×D5 | semidirect |
| 82. C2×C52 | #117 | semidirect |
| 116. C4×D5 | C2×Dic5 | semidirect |
| 123. C52 | C2×#117 | semidirect |
| 164. C2×C5 | #4018 | semidirect |
| 165. C2×C5 | #4072 | semidirect |
| 185. C5 | C2×#4018 | semidirect |
| 186. C5 | C2×#4072 | semidirect |
| 198. C2 | #11716973 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C2×C4×#1039 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×#87780 | 2 |
| C2×#87778 | 2 |
| #11716973 | 2 |
| C2×#4072 | 5 |
| C2×#4018 | 5 |